1. Historical Background. - 2. Modern Developments. - 1: Some Basic Concepts. - 1. 1. Definitions. - 1. 2. Green's Identities. - 1. 3. Distributions. - 1. 4. Fundamental Solutions. - 2: Linear Elliptic Operators. - 2. 1. Constant Coefficients. - 2. 2. Laplace Operator. - 2. 3. Helmholtz Operator. - 2. 4. Cauchy-Riemann Operator. - 2. 5. Nonhomogeneous Operator. - 2. 6. Maximum Principle. - 2. 7. Method of Images. - 3: Linear Parabolic Operators. - 3. 1. Diffusion Operator. - 3. 2. Heat Potentials. - 3. 3. Cauchy Problem. - 3. 4. Maximum Principle. - 3. 5. Schrödinger Operator. - 3. 6. Method of Images. - 4: Linear Hyperbolic Operators. - 4. 1. Wave Operator. - 4. 2. Harmonie Oscillators. - 4. 3. Wave Potentials. - 4. 4. Cauchy Problem. - 4. 5. Wave Propagation. - 4. 6. Maxwell's Equations. - 5: Nonlinear Operators. - 5. 1. Einstein-Kolmogorov Operator. - 5. 2. Fokker-Plank Operator. - 5. 3. Klein-Gordon Operator. - 5. 4. Dirac's Operator. - 5. 5. Transport Equation. - 5. 6. Transport Operator. - 5. 7. Biharmonic Operator. - 5. 8. Nonlinear Wave Equations. - 5. 9. The ?-function. - 5. 10. Quasihyperbolic Operator. - 6: Elastostatics. - 6. 1. Basic Relations. - 6. 2. Cauchy-Navier Operator. - 6. 3. Half-Space Solutions. - 6. 4. Axisymmetric Solutions. - 6. 5. Somigliana's Identity. - 7: Elastodynamics. - 7. 1. Elastodynamic Operator. - 7. 2. Wave Structures. - 7. 3. Bernoulli-Euler Operator. - 7. 4. Elastoplasticity. - 7. 5. Anisotropic Medium. - 8: Fluid Dynamics. - 8. 1. Navier-Stokes Equations. - 8. 2. Aerodynamic Flows. - 8. 3. Non-Newtonian Flows. - 8. 4. Porous Media. - 8. 5. Underwater Acoustic Scattering. - 9: Piezoelectrics. - 9. 1. Green's Functions. - 9. 2. Dynamic Piezoelectric Operator. - 9. 3. Fundamental Solutions. - 9. 4. Steady-State Solutions. - 9. 5. Piezocrystal Waves. - 10: Boundary Element Methods. - 10. 1. Boundary Integral Equations. - 10. 2. BoundaryElement Method. - 10. 3. Poisson Equation. - 10. 4. Transient Fourier Equation. - 10. 5. Laplace Transform BEM. - 10. 6. Elastostatic BEM. - 10. 7. Fracture Mechanics. - 11: Domain Integrals. - 11. 1. Dual Reciprocity Method. - 11. 2. Multiple Reciprocity Method. - 11. 3. Transient DRM. - 11. 4. Transient MRM. - 11. 5. Fourier Series Method. - 11. 6. Complex Variable BEM. - 12: Finite Deflection of Plates. - 12. 1. von Karman Equations. - 12. 2. Boundary Integral Equations. - 12. 3. Large Deflections. - 12. 4. Singularities in Biharmonic Problems. - 13: Miscellaneous Topics. - 13. 1. Poroelasticity. - 13. 2. Heat Conduction. - 13. 3. Thermoelasticity. - 13. 4. Neutron Diffusion. - 13. 5. Biomechanics. - 14: Quasilinear Elliptic Operators. - 14. 1. p-Laplacian. - 14. 2. Lane-Emden Equation. - 14. 3. Emden-Fowler Equation. - 14. 4. Black Hole Solutions. - 14. 5. Einstein-Yang-Mills Equation. - Appendix A: Transforms of Distributions. - A. 1. Fourier Transform. - A. 2. Laplace Transform. - A. 3. Inverse Laplace Transform. - Appendix B: Computational Aspects. - Appendix C: List of Differential Operators. Language: English